A rise of 5-10 psi shows the rings are not sealing like they should, but really bad rings would show a 20 psi or more increase. It is going to be difficult to do more diagnostics on the cylinders without compressed air. There appears to be something wrong with the engine (a timing chain that has jumped a tooth and/or bent valves can also show low compression, in addition to a bad head gasket). Since you have even low compression in all cylinders I'm leaning toward valves and/or the timing chain has jumped a tooth - something along these lines anyway. A blown head gasket will usually show 1-2 bad cylinders and not all cylinders being equally low on compression.
It can be really hard to diagnosis a problem via email when you can't do more tests (I recall a person cussing me out when I could not ID the problem with his engine by listening to it over the telephone and he refused to bring it to the shop because he claimed we would rip him off repairing things that did not need to be fixed - true story!).
Is the starter turning fast enough to start the engine? It sounds like the car has not run for a while and a push start will get the engine turning fast enough to possibly start. However, if there is a mechanical problem with the engine push starting could do more damage (but, then again maybe not if the engine is already damaged - the rock and hard place position). If you try push starting, make sure you can get the car back home if the engine fails to start.
I suggest that you continue to inspect the things I listed. Do you have a shop manual to help with specs needed to inspect relationships/condition etc. to determine what the problem is? The Haynes manual for your model probably has a good trouble shooting section - the ones I've looked at do, but I have not looked at the Haynes manual for your model.
It may come to having to do a TDI (tear down and inspection) to find the problem. However, personally I would want to do more tests to see if something else is the problem since 120 psi compression is close to minimum needed for an engine to run and it sounds like this car has not run for a while.
Perhaps another member has had a similar problem and can help you.
America: Land of the Free!
1977 300D: 300,000+ miles
American Honda: Factory Trained Technician & Honor Grad.
Technical Advisor to Am. Honda;
Supervisor of Maintenance largest tree care co. in US for offices in Tex.